Related papers: Robust Quantum Error Correction via Convex Optimiz…
Implementing quantum error correction (QEC) protocols is a challenging task in today's era of noisy intermediate-scale quantum devices. We present quantum circuits for a universal, noise-adapted recovery map, often referred to as the Petz…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
The recently introduced Quantum Lego framework provides a powerful method for generating complex quantum error correcting codes (QECCs) out of simple ones. We gamify this process and unlock a new avenue for code design and discovery using…
It is shown that the noise process in quantum computation can be described by spatially correlated decoherence and dissipation. We demonstrate that the conventional quantum error correcting codes correcting for single-qubit errors are…
Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore…
In this paper, we provise an implementation of five, seven and nine-qubits error correcting codes on a classical computer using the quantum simulator Feynman program. We also compare the three codes by computing the fidelity when double…
Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
A quantum channel models the interaction between the system we are interested in and its environment. Such a model can capture the main features of the interaction but because of the complexity of the environment we can not assume that it…
The use of analog classical systems for computation is generally thought to be a difficult proposition due to the susceptibility of these devices to noise and the lack of a clear framework for achieving fault-tolerance. We present…
Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on…
Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the…
In this paper, we address the problem of designing a quantum encoder that maximizes the minimum output purity of a given decohering channel, where the minimum is taken over all possible pure inputs. This problem is cast as a max-min…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across…
We propose quaternion-based strategies for quantum error correction by extending quantum mechanics into quaternionic Hilbert spaces. Building on the properties of quaternionic quantum states, we define quaternionic analogues of Pauli…